In fluorescence-based DNA analyzers, fluorescence spectra are acquired by exciting the sample during the analysis/assay. The information of interest, e.g., called bases or genotypes, is generated by transforming the fluorescence spectra acquired during analysis/assay to “dye amounts,” i.e., how much of each dye is present or being generated during the analysis/assay.
Consider, for example, the simple case of determining the amounts of two dyes present in a solution using spectral sensors. The fluorescence emission at each spectral sensor (wavelength region or CCD bin) is the sum of the contributions of each dye. This can be expressed mathematically as:Signal at sensor i=Emission of Dye 1 at sensor i+Emission of Dye 2 at sensor i  (I)The first thing to note about equation (I) above is that it contains one known quantity (measured signal at sensor i), and two unknown quantities (the emission of each dye at sensor i). Since there is one equation having two unknowns, no unique solution can be found. It is important to note that including more sensors (for example a second sensor j) is not necessarily helpful because each sensor adds an equation similar to equation (I) with two unknown quantities, namely the contributions of the individual dyes to the signal acquired at the sensor. In order to determine the amounts of two dyes in a solution more information is needed.
The additional information that enables a determination of the amounts of two dyes in a solution comes from the physical laws of fluorescence emission. FIG. 2 shows a typical emission intensity profile as a function of dye amount at a spectral sensor. (FIG. 2 is also referred to as the dye response function.) The segment of the dye response function that shows a linear relationship between the emission intensity at the spectral sensor and the dye amount is also referred to as the linear response range (or linear range). In FIG. 2, this range is from dye amount=1 to dye amount=5. In practice, experimental and sample conditions are optimized such that the analysis/assay is performed in this range. Under these conditions, the emission of any dye at any sensor is equal to the product of the amount of dye and the slope of the response function in the linear range. The slope of the dye's response function in the linear range is determined by the physical nature of the dye and is also known as the sensitivity. For a pure dye and a specific spectral sensor, the sensitivity is a physical constant over a given range of dye amounts. Equation (I) can thus be expressed as:Signal at sensor i=Ki1*A1+Ki2*A2  (II)where Ki1 is the sensitivity of dye 1 at sensor i,                A1 is the amount of dye 1,        Ki2 is the sensitivity of dye 2 at sensor i, and        A2 is the amount of dye 2.There are now four unknown quantities (Ki1, Ki2, A1 , and A2) to determine. Two of these unknowns (A1 and A2) depend on the sample. The other two unknowns (Ki1 and Ki2) depend on the nature of the dye and the spectral sensors and thus can be estimated independent of the sample by what is referred to as spectral calibration.        
Spectral calibration is thus the process by which the sensitivity of each dye is determined at each sensor. Doing so enables us to estimate the parameters that are needed to analyze samples independent of the samples. Continuing with our example of estimating the amount of two dyes in a sample in a solution, equations (3) and (4) express the measurements acquired at two sensors i and j in relation to the dye amounts of interest A1 and A2:Signal at sensori=Ki1*A1+Ki2*A2  (III)Signal at sensorj=Kj1*A1+Kj2*A2  (IV)where Ki1, A1, Ki2 and A2 are as defined above (Equation (II)) and
Kj1 and Kj2 are the sensitivity at sensor j for dyes 1 and 2 respectively.
To determine A1 and A2 using equations (III) and (IV), we first estimate Ki1, Ki2, Kj1 and Kj2 using pure dyes. Then we solve equations (III) and (IV) to estimate A1 and A2. The process of estimating Ki1, Ki2, Kj1 and Kj2 using pure dyes is known as spectral calibration. The process of using Ki1, Ki2, Kj 1, Kj2, Signal at sensor i and Signal at sensor j to estimate A1 and A2 is known as multicomponent analysis.
Equations (III) and (IV) can be expressed in linear algebraic from as:                               [                                                                      S                  ⁢                                                                          ⁢                  i                  ⁢                                                                          ⁢                  g                  ⁢                                                                          ⁢                  n                  ⁢                                                                          ⁢                  a                  ⁢                                                                          ⁢                  l                  ⁢                                                                          ⁢                  a                  ⁢                                                                          ⁢                  t                  ⁢                                                                          ⁢                  s                  ⁢                                                                          ⁢                  e                  ⁢                                                                          ⁢                  n                  ⁢                                                                          ⁢                  s                  ⁢                                                                          ⁢                  o                  ⁢                                                                          ⁢                  r                  ⁢                                                                          ⁢                  i                                                                                                      S                  ⁢                                                                          ⁢                  i                  ⁢                                                                          ⁢                  g                  ⁢                                                                          ⁢                  n                  ⁢                                                                          ⁢                  a                  ⁢                                                                          ⁢                  l                  ⁢                                                                                                    ⁢                                                                                                  ⁢                  a                  ⁢                                                                          ⁢                  t                  ⁢                                                                          ⁢                  s                  ⁢                                                                          ⁢                  e                  ⁢                                                                          ⁢                  n                  ⁢                                                                          ⁢                  s                  ⁢                                                                          ⁢                  o                  ⁢                                                                          ⁢                  r                  ⁢                                                                          ⁢                  j                                                              ]                =                              [                                                                                K                    ⁢                                                                                  ⁢                    i1                                                                                        K                    ⁢                                                                                  ⁢                    i2                                                                                                                    K                    ⁢                                                                                  ⁢                    j1                                                                                        K                    ⁢                                                                                  ⁢                    j2                                                                        ]                    ⁢                                          [                                                    A1                                                                    A2                                              ]                                    (        V        )            The matrix containing Ki1, Ki2, Kj1 and Kj2 is referred to as the calibration matrix.
To summarize, pure dyes are used to determine the calibration matrix (Ki1, Ki2, Kj 1 and Kj2 above). This is known as spectral calibration. The calibration matrix is subsequently used to analyze samples according to equation (V) above.
For more details on the above background materials, see for example M. A. Sharaf, D. L. Illman and B. R. Kowalski, Chemometrics, Wiley, N.Y., 1986, Chapter 4 (p119–p147).
Charge Coupled Devices (CCD) can be used to detect emission spectra of fluorescent dyes. A CCD-based detector can be employed in a variety of configurations. For example, the CCD can be set up to cover the spectral range of interest as an array whose elements detect discrete regions of the spectral wavelength range of interest. FIG. 3, for example, shows an example of an emission spectrum (top panel, blue line), and 24 discrete regions in the wavelength domain. (top panel, red lines). Each of the 24 discrete regions is referred to as a spectral bin. In this example, the wavelength range from 530 nm to 650 nm is divided into 24 spectral bins of 5 nm each.
The bottom panel of FIG. 3 represents the spectral intensities as depicted on the CCD. The term “spectral channel” is often used to refer to a “spectral bin.”
As has been discussed, spectral calibration is to estimate reference spectral profiles (reference spectra) of particular fluorescent dyes using the optical measurement system of an automated DNA sequencer or similar fluorescent polynucleotide separation apparatus where the particular dyes will be utilized. The current practice of spectral calibration relies on measuring the spectral profile of each fluorescent dye separately. This approach to spectral calibration of fluorescent polynucleotide separation apparatus results in reduced throughput because it requires N lanes on gel-based instruments and requires N separate runs on capillary-based instrument. As more fluorescent dyes are developed and utilized routinely (N is expected to increase), the spectral calibration of fluorescent polynucleotide separation apparatus becomes more demanding and less efficient under the current practice. Additionally, the amount of computer resources devoted to spectral calibration also increases with the number of dyes and separation channels analyzed.